Estimation of Forest Stock Volume in Complex Terrain Using Spaceborne Lidar

Abstract

In forest remote sensing monitoring of complex terrain, spaceborne lidar data has become a key technology for obtaining large-scale forest structure parameters due to its uniquethree-dimensional observation capabilities. However, in complex terrain conditions, there are still many challenges for spaceborne lidar. Particularly in mountainous forest areas with significant topographic relief, overcoming the limitations imposed by complex terrain conditions to achieve high-precision forest stock volume estimation has emerged as one of the most challenging and cutting-edge research areas in vegetation remote sensing. Objective: This study aims to explore the feasibility and methods of forest stock volume estimation using spaceborne lidar data ICESat-2/ATL08 in complex terrain and to compare the effectiveness of three machine learning regression models for this purpose. Method: Based on the ATL08 product from ICESat-2/ATLAS data, a sequential Gaussian conditional simulation was used for spatial interpolation of forest areas in Jingdong Yi Autonomous County, Pu’er City, Yunnan Province. XGBoost, LightGBM, and Random Forest methods were then employed to develop stock volume models, and their estimation capabilities were analyzed and compared. Results: (1) Among the 57 ICESat-2/ATLAS footprint parameters extracted, 13 were retained for interpolation after analysis and screening. (2) Based on sequential Gaussian conditional simulation, three parameters demonstrating lower interpolation accuracy were eliminated, with the remaining ten parameters allocated for inversion model development. (3) In terms of inversion model accuracy, XGBoost outperformed LightGBM and Random Forest, achieving an R² of 0.89 and an rRMSE of 10.5912. The average forest stock volume derived from the inversion was 141.00 m³/hm². Conclusions: Overall, large-area forest stock volume estimation through spaceborne Lidar inversion using ICESat-2/ATLAS photon-counting footprints proved feasible for mountainous environments with complex terrain. The XGBoost method demonstrates strong forest stock volume inversion capabilities. This study provides a case study for investigating forest structure parameters in complex mountainous terrain using spaceborne lidar ICESat-2/ATLAS data.

1. Introduction

Forests are essential components of global ecosystems, providing critical functions such as carbon sequestration, biodiversity maintenance, and climate regulation. They support the survival and evolution of both human societies and other species. Forests are characterized by high biodiversity, which sustains complex ecosystem structures and efficient nutrient cycles. Secondly, forests are hailed as the most valuable comprehensive treasure trove in nature, possessing multiple key functions such as carbon storage, gene preservation, resource reserve, water conservation, and energy accumulation. Finally, forests play an irreplaceable role in environmental protection. They not only optimize the quality of the ecological environment but also maintain the dynamic balance of the global ecosystem, providing a fundamental environmental guarantee for the sustainable development of human society [1,2]. Forest is the main component of the terrestrial biosphere, playing a crucial role not only in maintaining regional ecological environments but also in significantly contributing to the global carbon balance [3,4,5]. Forest stock volume (FSV) quantitatively represents the aggregate stemwood volume of all viable standing trees within a delineated forest area, usually expressed in volume units. It is an important indicator for measuring the scale of forest resources and the potential for timber production, as well as a key basis for evaluating the ecological functions of forests [6].

In the past, forest resource surveys relied on time-consuming and labor-intensive manual inventory methods. For example, the traditional measurement of forest stock volume involved measuring tree height, diameter at breast height, and other stand parameters, and establishing a corresponding volume equation to calculate the forest stock volume. Common methods for measuring forest stock volume include the standard tree method and the volume table method. The standard tree method estimates forest stock volume based on the representativeness of the standard tree. If the standard tree does not represent the entire forest, it may lead to estimation errors, and a certain number of trees need to be felled, which can easily cause forest damage. Manual inspection methods are especially difficult in complex mountainous environments. Although optical remote sensing can achieve large-scale forestry monitoring, it can only capture features of the forest canopy surface and struggles to acquire its vertical structure characteristics. Furthermore, the mountainous terrain often experiences variable weather conditions with frequent cloud cover, and data loss or degradation is especially likely during the rainy season. Compared to optical remote sensing, LiDAR technology directly measures the three-dimensional structure of forests, offering significant potential for forest resource management and ecosystem research. However, large-scale continuous observation is challenging with airborne or near-ground LiDAR platforms (e.g., stationary, mobile, and unmanned aerial vehicles). While airborne LiDAR offers high precision and efficiency, it has limitations. Complex mountainous terrain (steep slopes and deep valleys) presents high flight safety risks for UAVs, making some areas difficult to access. Synthetic Aperture Radar (SAR) enables all-weather, high-resolution observations with superior penetration capabilities, making it indispensable for resource exploration, environmental monitoring, and related geoscientific applications [7]. However, SAR produces pixel layover in steep slope areas, resulting in severe geometric distortion. Furthermore, topographic relief causes drastic variations in local incidence angles, and backscatter from identical land-cover types varies with slope, necessitating DEM-based terrain correction. However, residual errors after correction still impact interpretation accuracy. Spaceborne LiDAR refers to a LiDAR system mounted on a satellite or spacecraft. It offers advantages such as low operational costs, high spatiotemporal data resolution, strong resistance to interference, and the ability to perform continuous and accurate monitoring of forest resources across regional areas at various spatiotemporal scales with high efficiency. It detects characteristic information of the ground or atmosphere through the emission and reception of laser pulses, generating three-dimensional point cloud data and high-precision terrain/surface elevation data. Its laser range is based on the time-of-flight principle and is unaffected by geometric distortions like SAR layover and foreshortening. Accurate surface elevation data can still be acquired in steep slope areas. Unlike traditional ground surveys, the proposed method delivers data of higher spatial resolution and accuracy. Such capability significantly improves the precision of forest growing stock quantification by overcoming key methodological constraints inherent to conventional techniques.

Currently, there are four Earth observation satellites globally equipped with LiDAR. The National Aeronautics and Space Administration (NASA) has launched three of them: ICESat-1 (Ice, Cloud, and Elevation Satellite-1) launched in 2003, ICESat-2 (Ice, Cloud and land Elevation Satellite-2) launched in 2018, and GEDI (Global Ecosystem Dynamics Investigation) launched in 2018. Additionally, China launched the Gaofen-7 (GF-7) in 2019. ATLAS aboard ICESat-2 employs micropulse multibeam photon-counting technology and serves as a full-waveform LiDAR payload. This provides a reliable foundation for extracting forest structures with high-precision data. Its global coverage capability and short repeat observation cycle make it suitable for large-scale dynamic monitoring of forests, especially in areas lacking ground survey data. These advantages make it an important tool for forest resource investigation and ecological research, particularly in monitoring forests in large-scale and complex terrain regions, where they play an irreplaceable role. Before the public release of ICESat-2 data, Neuenschwander and others used simulated ICESat-2 data to explore the accuracy of the ATL08 algorithm in retrieving forest canopy height, which showed a significant correlation with airborne point cloud data. The root-mean-square error (RMSE) in the Alaska permafrost/taiga transition zone and Sonoma County, California, was less than 2 m [8]. Since NASA officially released the ICESat-2/ATLAS satellite data on 30 May 2019, researchers have systematically investigated the retrieval of forest structural parameters utilizing this satellite-derived dataset [9]. Zhu effectively reduced the discrepancies in forest height obtained by GEDI and ATLAS by constructing a forest height consistency model. By processing encrypted ICESat-2 point clouds alongside Sentinel-2 multispectral data, researchers created a continental-scale forest height product (30 m grid) exhibiting 2.67 m RMSE relative to ground truth plots [10]. There are certain differences in the inversion performance between ICESat-2/ATLAS and GEDI. Liu et al. demonstrated that ATLAS has higher accuracy in topographic mapping than GEDI, while GEDI performs better in canopy height mapping [11]. ATLAS and GEDI now serve as primary data sources for most forest canopy height inversion research. Concurrently, multi-source data integration techniques have gained widespread application in producing high-resolution forest canopy height maps.

The use of ICESat-2/ATLAS data for forest structure parameter inversion holds significant application potential. However, there is still a need for in-depth exploration on how to improve the inversion accuracy in forest stock volume inversion under large-scale complex mountainous terrain conditions, and this area remains under-researched. LiDAR technology, since its inception in the 1960s, has been classified as active remote sensing technology due to its principle of actively emitting probing beams towards objects. The accuracies mentioned below refer to the degree of consistency between the predicted results and the ground survey data. It effectively acquires 3D information within the canopy and is increasingly used in various disciplines such as surveying and forestry [12]. From the perspective of data sources, LiDAR addresses the saturation issues that traditional optical remote sensing and SAR remote sensing data are prone to, demonstrating its unique advantages in reflecting forest structures. However, LiDAR is susceptible to slope factors in areas with complex terrain. In steep slopes, the angle of incidence of the laser pulse varies greatly, resulting in an uneven distribution of the point cloud [13], and the larger the slope, the more pronounced the laser footprint distortion [14]. Steeply sloping terrain may result in multiple reflections of the laser beam, making the point cloud data noisy, and in extreme terrain (e.g., cliffs and deep valleys), the elevation error of LiDAR may increase significantly. Holmgren et al. used two regression models to estimate stocking in a sample plot with a radius of 10 m. The first model used the LiDAR-estimated tree height and canopy area as variables (coefficient of determination (R²) = 0.9, RMSE = 22% of the mean forest stock volume), while the second model used the LiDAR-estimated tree height and number of plants as variables (R² = 0.82, RMSE = 26% of the mean forest stock volume). The study concluded that tree height and forest stock volume can be estimated at a high spatial resolution (10 m radius plots) in forested areas using LiDAR data in combination with ground sample surveys. The research site is positioned in southern Sweden, with flat terrain and elevations between 120 and 145 m above sea level, and the inversion model has a high accuracy [15]. Pang Yong and his colleagues established a model based on the upper quartile tree height (H75) of the highly normalized point cloud and the field survey data, then inverted the average stand height in the study area. A density-gradient experimental design was implemented to assess point cloud sparsity effects, with paired t-tests demonstrating statistically distinct outcomes (p < 0.01) for canopy height and DBH estimation across density regimes. It was found that high-density point clouds can enable further individual tree segmentation based on the CHM, thus reducing the reliance on measured data. The study area of this research is located in forest farms in Shandong and Chongqing, where the terrain is relatively gentle. The average accuracy in the Shandong study area reaches 90.59%, indicating excellent results [16]. Dong et al. used the ICESat-1/GLAS data to invert the maximum height of the forest canopy and developed an extrapolation model to estimate the aboveground biomass at the regional scale. The results indicated that the estimation accuracy of the forest canopy top height and aboveground biomass was relatively high, with the R² for the forest canopy top height being 0.69. The study area of this research was the Three Gorges Reservoir Area, situated at the junction of the second and third topographic steps. The complex terrain in this area resulted in relatively low inversion accuracy [17]. Wang et al. systematically analyzed ICESat-1/GLAS full-waveform data to investigate the interplay between lidar-derived canopy height metrics, in situ measured tree heights, and terrain slope characteristics. Their study revealed significant slope-dependent biases (p < 0.01) in spaceborne lidar height measurements while establishing robust allometric relationships (R² = 0.78) between median canopy height attributes and forest stand volume. Through comprehensive waveform processing and statistical validation, the researchers quantified the impact of topographic variation on height estimation accuracy and developed predictive models linking remote sensing metrics to forest biomass parameters. The results showed that the slope was well-correlated with both the measured average tree height and the forest stock volume. The ICESat-1/GLAS data had certain potential in estimating forest stock volume. Meanwhile, it was found that the error in the tree height estimated by lidar data would also increase as the slope increased [18]. In 2013, Neigh et al. estimated the aboveground biomass and carbon storage of boreal forests using ICESAT-1/GLAS data. The estimated total aboveground carbon was 38 ± 3.1 Pg. The study indicated that the slope calculation in the research could affect the accuracy of the estimation [19]. Liu et al. combined ICESat-2 and Sentinel-2A data in 2023 to conduct an inversion of forest stock volume in Shangri-La, which was chosen as the study area. The results show that when the Sentinel-2A and ICESat-2/ATLAS variable sets are combined, the Random Forest method achieves the highest inversion accuracy, with an R² value of 0.7034. The study area features typical complex terrain with significant undulations. The complex geographical environment will reduce the inversion accuracy [20].

This study took ICESat-2/ATL08 as the primary data source and Jingdong Yi Autonomous County, Pu’er City, Yunnan Province, as the study area. It conducted research on issues such as forest stock volume inversion under complex terrain conditions using spaceborne lidar. We generated a spatial distribution map of forest stock volume in the study area to underpin forest resource management and monitoring, biomass and carbon storage quantification, ecosystem health assessment, and biodiversity evaluation. The core innovation of this study lies in its systematic evaluation of the performance and methodological applicability of spaceborne lidar (ICESat-2/ATLAS) for forest stock volume inversion in topographically complex mountainous regions. In response to the challenges posed by rugged terrain and limited remote sensing detection conditions in mountainous environments, this research adopts inversion algorithms specifically tailored for complex landscapes. The approach demonstrates a certain degree of improvement in the monitoring accuracy of spaceborne lidar in highly heterogeneous forest areas. Furthermore, it offers a novel technical pathway to address the long-standing issues of “data scarcity” and “insufficient accuracy” in mountain forest resource surveys.

2. Overview of the Study Area and Data Sources

2.1. Overview of the Study Area

Jingdong Yi Autonomous County is positioned in the western subregion of Yunnan Province and the northern sector of Pu’er City, with the Lancang River to its eastern boundary and the Ailao Mountains forming its western border. Its geographical coordinates range from 100°24′ to 101°15′ east longitude and 23°57′ to 24°50′ north latitude. It extends 73 km from north to south and 61 km from east to west. The total land area of the county is 446,585 hectares. The geographical location of the research area is shown in Figure 1, and the topography, water system, and road schematic diagram are presented in Figure 2.

Jingdong County is located in the central-western part of Yunnan Province and at the northern end of Pu’er City. It lies at the southern tip of the Hengduan Mountains. Jingdong Yi Autonomous County, located in western Yunnan and northern Pu’er, is defined by its mountainous terrain and strategic geographic position between the Lancang River and Ailao Mountains. The Wuliang Mountain, as a key topographic feature, is the southwestern offshoot of the Yunling Mountains, running north–south and extending southward to the national border. The Ailao Mountain is the southward offshoot of the Yunling Mountains, stretching southward to the national border. The Daque Mountain lies between the Wuliang Mountain and the Ailao Mountain. It is a branch range of the Ailao Mountain, running parallel to the Ailao Mountain and extending southward from Jingdong to Zhenyuan County. The Wuliang Mountains and the Ailao Mountains are the outlying ranges of the Hengduan Mountains. The Ailao and Wuliang Mountains stand opposite each other, east to west, with rolling peaks stretching as far as the eye can see. As one descends from the mountaintops to the foothills, the terrain gradually flattens out with the decreasing altitude. The region features a significant relative elevation difference. The highest point (the summit of Maotou Mountain and the peak of the Wuliang range) soars to 3371 m, while the lowest point (the confluence of the Wenxiao River in Dachao East Town and the Lancang River) lies at 795 m, a staggering difference of 2511 m. This area takes on a distinctive north–narrow, south–broad topography, sloping gently from north to south. Characterized by lofty ridges, precipitous slopes, and deep valleys, the landscape is a sea of undulating mountains, with the north being higher than the south. From the lowest to the highest elevations, one can find valleys, hills, and mountains, typifying a deeply dissected mid-mountain terrain. The region’s abundant mountain ranges, massive peaks, high altitudes, deeply incised river valleys, substantial changes in elevation, and complex topographical features have fostered a rich tapestry of plant species and vegetation types, which are clearly distributed along an altitudinal gradient.

According to the classification standard of forestry slope grades, we conducted a graded statistical analysis. The slopes were categorized into five grades: Grade I represented the gentlest slope (≤5°), Grade II represented a relatively gentle slope (6–15°), Grade III represented an ordinary slope (16–25°), Grade IV represented a relatively steep slope (26–35°), and Grade V represented a steep slope (>35°). Figure 1 shows the slope distribution in Jingdong County, where the maximum slope was 88.91° and the average slope was 22.82°. In most areas, the slope ranged from 15° to 25°.

2.2. Data

2.2.1. ICESat-2

The ICESat-2 (Ice, Cloud and land Elevation Satellite-2) is an Earth-observing satellite developed by the U.S. National Aeronautics and Space Administration (NASA). The primary mission of this satellite involves delivering highly accurate elevation data, as well as monitoring dynamic changes in polar ice sheets, sea ice thickness, and global forest vegetation. It holds significant scientific importance for understanding the mass balance changes in sea ice in the Arctic and Antarctic, as well as for global biomass estimation. The Advanced Topographic Laser Altimeter System (ATLAS) instrument aboard ICESat-2 utilizes innovative micropulse, multibeam photon-counting lidar technology. Operating in a non-sun-synchronous orbital configuration at an average altitude of 500 km, the system achieves near-global observational coverage from 88° north to 88° south latitude. Notably, the satellite maintains a precise 91-day exact repeat cycle for systematic Earth observation. The ATL08 data from ICESat-2 is a crucial data product provided by the satellite, acquiring detailed information on surface elevation and vegetation height through high-precision laser measurement technology. It has extensive applications in fields such as forest biomass estimation, glacier and ice cap monitoring, and terrestrial elevation measurement. The study conducted an inversion of forest stock volume based on ATL08 photon data, using Jingdong Yi Autonomous County, Pu’er City, Yunnan Province, as the research area. The ATL08 data products from January to December 2019 within the Jingdong County area were selected, totaling 32 datasets, 96 tracks, and 192 photon track beams, all in H5 format. The scientific data products generated by ICESat-2 are publicly accessible and available for download through the mission’s official data portal hosted by the National Snow and Ice Data Center (NSIDC) at https://nsidc.org/data/atl08/versions/6 (accessed on 7 June 2024).

The topographic data used in this study was extracted using a digital elevation model (DEM). The DEM adopted publicly available 30 m resolution DEM data released by the National Aeronautics and Space Administration (NASA), and the data was downloaded from the Geospatial Data Cloud (http://www.gscloud.cn/)(accessed on 7 June 2024). In terms of data processing, the slope topographic factor of the study area was extracted using ArcMap (v10.8) software.

2.2.2. Ground Survey Data

In forestry management systems, the term “second-type survey” serves as the standardized abbreviation for forest resource planning and design surveys. The technical methods of forest management surveys mainly include comprehensive visual inspection, sub-compartment delineation, sample plot surveys, etc. During the survey process, forest resources are usually divided into several sub-compartments through sub-compartment delineation, and detailed surveys are conducted on a sub-compartment basis. Meanwhile, a certain number of sample plots will also be set up for detailed surveys as needed to obtain more accurate forest resource data. The forest inventory data utilized in this study were obtained from angle-gauge sampling plots established during the second-class forest resource survey conducted in Jingdong County. Field measurements for these sample plots were systematically collected during the spring season of 2016 (March to May). In the study area, sample plots were established using a mechanical sampling method with an east–west spacing of 3 km and a north–south spacing of 4 km. A total of 370 sample plots were set up, including 270 in arbor forests, 2 in bamboo forests, 28 in shrub forests, 14 in non-established forests, 4 in logged areas, and 62 in non-forested areas. The sample plots recorded parameters such as the central coordinates of the sample points, sub-compartment land types, dominant tree species, tree height, and forest stand volume. After eliminating sample plots with no forest volume and outlier plots, 212 sample plots were ultimately selected for the study. The forest stand volume characteristics derived from the 212 systematically sampled plots are summarized in

Table 1. Descriptive statistics of plot forest stock volume.

Number of Sample Plots	Min	Max	Mean	Standard Deviation
212 (plots)	10.8 m3/hm2	361.8 m3/hm2	139.3 m3/hm2	69.5 m3/hm2

, presenting key statistical parameters of the inventory dataset.

3. Methods

The main content of this study, which involves the construction of the ICESat-2/ATLAS study area’s forest stock volume inversion model, includes extracting and selecting model variables, constructing the forest stock volume inversion model, and validating the prediction accuracy of inversion results against field plot measurements.

Through systematic spatial analysis, the research generated a comprehensive forest stock volume distribution map that visually characterizes the spatial patterns of woody biomass throughout the investigated region. The complete methodological workflow, including data processing and analytical procedures, is illustrated in Figure 3.

3.1. Parameter Screening

Based on the Python 3.8, Different Densities-Based Spatial Clustering of Applications with Noise (DDBSCAN) and K-nearest neighbors-based (KNNB) are employed to filter noise photons in high and low backgrounds. Subsequently, the Progressive TIN Densification (PTD) is used to classify the denoised photons. Photons with erroneous parameters and poor signal quality are then manually removed, resulting in 8855 valid photons. The distribution of these valid photons is shown in Figure 4.

The selection of feature variables is fundamental for forest stock volume inversion. By studying and analyzing various data types, appropriate feature variables can be chosen to reduce redundancy in the model. The parameter selection in this study is mainly based on empirical results from the existing literature. A systematic review of research in related fields (such as the studies by Liu, MY. et al. [20] and Du, J. et al. [21]) revealed that parameters such as h_mean_canopy, dem_h, and h_te_best_fit are commonly used in studies of forest structure parameters. Supported by the existing literature, since variogram analysis requires improving model convergence and determining whether parameters conform to a normal distribution, the study parameters and their respective operational definitions are systematically summarized in

Table 2. Data product parameters of ICESat-2/ATL08 [22] (https://nsidc.org/data/ICESat-2) (accessed on 7 June 2024).

Data_Rate	Long_Name	Description
dem_h	dem height	The value corresponds to the highest-priority DEM (Arctic > Antarctic > Global > MSS) available at the given coordinates, with heights referenced to the WGS84 ellipsoid (units: meters).
h_canopy_uncertainty	segment canopy height uncertainty	The uncertainty of relative canopy heights for the segment incorporates both systematic uncertainties and photon identification errors.
h_canopy_abs	absolute segment canopy height	The upper canopy elevation threshold (98th percentile) is georeferenced to the WGS84 datum.
h_canopy_quad	canopy quadratic mean	The second-order moment of the vegetation photon height distribution above the modeled terrain.
h_mean_canopy_abs	absolute mean canopy height	Mean absolute canopy height within the segment (referenced to WGS84 ellipsoid).
n_ca_photons	number canopy photons	Count of canopy-top-classified photons per segment.
h_median_canopy	median canopy height	The median relative canopy height within the segment (equivalent to RH50 in the literature).
terrain_slope	segment terrain slope	The along-track terrain slope per segment, derived from linear regression of terrain-classified photons.
centroid_height	centroid height	Optical centroid of canopy- and ground-classified photons within the segment.
h_te_interp	Interpolated terrain surface height	Interpolated terrain height at segment midpoint (WGS84 ellipsoid reference).
h_te_best_fit	segment terrain height best fit	The optimal terrain elevation values were derived through regression analysis at the centroid position of every 100 m longitudinal segment.
n_toc_photons	number top of canopy photons	Segment-aggregated canopy zenith photon density.
h_canopy_r	height canopy	The 98th percentile of segment-level canopy height differentials relative to the interpolated terrain surface.

.

3.2. Spatial Interpolation

3.2.1. Variogram

The variogram underpins the theoretical framework of simple kriging interpolation by quantifying the spatial autocorrelation of geographical data. Thanks to its flexible model construction method, it holds significant application value in related research [23], which is unique and determined by the model type, base value, Sill, Range, and Nugget. In a sequential Gaussian simulation (SGS), the variogram serves as a fundamental tool for characterizing the spatial dependence structure of geostatistical data. By fitting an optimal theoretical model tailored to the dataset and research objectives, it effectively captures the variability patterns of regional-scale variables. The choice of variogram model critically governs the realism and precision of the simulation outcomes.

Prior to variogram modeling, comprehensive data preprocessing is required to ensure optimal computational convergence. All input parameters must be standardized through min–max normalization, constraining values to either the unit interval [0, 1] or symmetric range [−1, 1], with subsequent evaluation of the distributional properties. When the Shapiro–Wilk test or other normality diagnostics indicate significant departures from Gaussian assumptions, application of a cube root transformation (also known as the Wilson–Hilferty transformation) is recommended to achieve approximate normality in the feature space. If they do not conform, a cube root transformation should be applied to make the data approximately follow a normal distribution. After this processing, the data can proceed to variogram analysis.

3.2.2. Sequential Gaussian Conditional Simulation (SGCS)

Sequential Gaussian conditional simulation (SGCS) is based on known data as the condition and uses the Monte Carlo method. It calculates the conditional expectation value of the point based on the joint distribution F(x) and the Monte Carlo method, obtaining the first simulation realization of this point. At each simulation position xm, F(x) is the cumulative conditional probability density function conditioned on n known data Z(xi), (i = 1, 2, …, n) and the previous m − 1 simulation values Z(xj), (j = 0, 1, 2, …, m − 1) [24]. These realizations not only conform to the statistical characteristics of the sample data (such as mean, variance, and variogram) but also reflect the uncertainty of spatial variables.

3.2.3. Accuracy Validation of Spatial Interpolation

This study performs K-fold cross-validation on the spatial interpolation results. By using multiple data partitions and averaging the evaluations, it provides a more reliable estimate of model performance. The evaluation metrics comprise RMSE (root-mean-square error) and R² (coefficient of determination). RMSE measures the standard deviation of prediction errors, representing the model’s absolute accuracy. R² evaluates the explained variance proportion, where values range from 0 to 1, with higher values denoting superior model fit.

3.3. Inversion Model for Regional Scale Forest Stock Volume and Accuracy Assessment

3.3.1. XGBoost

XGBoost (Extreme Gradient Boosting) was proposed by Chen at the 22nd ACM SIGKDD Conference [25]. XGBoost represents a prominent implementation of the boosting paradigm, where multiple weak learners are systematically combined to construct a powerful predictive model. This approach establishes a sequential dependency chain among base learners, necessitating an iterative training process where each new learner focuses on correcting the errors of its predecessors. The algorithm’s distinctive characteristic lies in this additive modeling strategy, where subsequent trees are specifically optimized to address the residual errors of the existing ensemble, progressively enhancing the overall predictive accuracy through carefully weighted combinations of sequentially generated weak learners. The tree model used is the CART regression tree model. XGBoost utilizes the first and second derivatives by performing a second-order Taylor expansion on the cost function, allowing for faster convergence on the training set and effectively improving training speed. Incorporating a regularization component into the objective function serves to constrain model intricacy while mitigating potential overfitting tendencies [26]. XGBoost is an additive model of decision trees. Based on its initial value, from the first to the k-th tree, the establishment of the next tree uses the prediction error of the previous iteration as a reference. The model’s final prediction is obtained through an additive combination of individual tree outputs in the ensemble. The expression of its algorithm model can be found in the reference literature [27].

3.3.2. LightGBM

LightGBM (Light Gradient Boosting Machine) is an efficient gradient boosting implementation that employs tree-based learning algorithms. It was proposed by Microsoft in 2015. The algorithm operates through an iterative process of training weak learners (typically decision trees) to progressively optimize model performance, which offers advantages such as strong training performance and a low risk of overfitting [28]. LightGBM employs a Histogram-based decision tree algorithm, which reduces the execution time of the GBDT algorithm. Additionally, its leaf growth strategy, with a maximum depth limitation, enhances the overall efficiency of the algorithm [29]. The expression of its algorithm model can be found in the reference literature [28].

3.3.3. Random Forest (RF)

Random Forest (RF), an influential ensemble learning method, was originally developed by Leo Breiman in 2001 [30]. Thanks to its excellent noise resistance and ability to process high-dimensional data, it has been widely applied in the regression modeling of forest parameters, for instance, stand height, biomass, and forest stock volume. Random Forest reduces overfitting and improves generalization by combining predictions from multiple decision trees. The expression of its algorithm model can be found in the reference literature [31].

3.3.4. Accuracy Assessment

To comprehensively assess the model’s effectiveness, this study employs the R² and the relative root-mean-square error (rRMSE) as metrics for assessing model accuracy and goodness of fit. The R² is a statistic used in regression analysis to quantify a model’s explanatory power, indicating the percentage of dependent variable variance accounted for by the independent variables. The rRMSE quantifies the magnitude of deviation between model predictions and observed values, normalizing this discrepancy relative to the range of actual values. The model’s two types of accuracy were evaluated using R² and rRMSE, respectively: explanatory accuracy (R²): whether the model has identified the correct relationships between variables; predictive accuracy (rRMSE): whether the errors of the model in practical applications are acceptable. This dual verification ensures the reliability of the model at both theoretical and practical levels.

4. Results and Analysis

The ATL08 product includes information such as the geographic coordinates, slope, elevation, and canopy height of photon points. In this study, 57 parameters from the spaceborne lidar ICESat-2/ATLAS were extracted, and the photon spots were screened and adjusted. Thirteen parameters that might affect accumulation and conform to a normal distribution were selected as feature variables to meet the requirements for interpolating discrete photon spots. Based on the accuracy verification results of spatial interpolation using sequential Gaussian conditional simulation, feature variables were selected. From the 57 feature variables extracted from the ICESat-2 ATL08 data, 10 feature variables were chosen. To explore the impact of different data on forest accumulation estimation, a variable set was constructed for modeling. The variable set was modeled using XGBoost, LightGBM, and RF to estimate forest stock volume, and the differences in inversion results obtained by different modeling methods were compared.

4.1. Feature Selection

Based on the accuracy verification results of spatial interpolation, three feature parameters with lower accuracy were excluded, leaving 10 feature parameters. The spatial interpolation accuracy of each parameter is shown in

Table 3. Spatial interpolation of ICESat-2/ATL08 eigen parameters.

Parameter	Distribution Type	Model	Number of Simulations	R2	RMSE
dem_h	log-normal distribution	Spherical model	110	0.9750	56.1027
h_canopy_abs	log-normal distribution	Spherical model	100	0.9718	59.8180
h_canopy_uncertainty	log-normal distribution	Exponential model	100	0.0745	40.9536
h_canopy_quad	log-normal distribution	Exponential model	100	0.2088	4.4481
h_mean_canopy_abs	log-normal distribution	Spherical model	120	0.9742	58.9860
h_median_canopy	log-normal distribution	Exponential model	100	0.0768	4.4222
terrain_slope	normal distribution	Exponential model	50	0.1557	0.2636
centroid_height	log-normal distribution	Spherical model	100	0.9721	59.2593
h_te_interp	log-normal distribution	Spherical model	120	0.9743	56.7864
h_te_best_fit	log-normal distribution	Spherical model	100	0.9738	57.2498

.

The contribution degrees of feature importance for each model are shown in Figure 5. From the contribution degrees of feature importance, it could be observed that in the establishment of the three models, features such as h_canopy_quad and h_canopy_uncertainty all had relatively high contributions. The importance of terrain_slope ranked among the top three in the LightGBM and RF models, while its proportion was relatively low in the XGBoost model.

4.2. Implement Sequential Gaussian Conditional Simulation (SGCS)

The optimal variogram for 13 ICESat-2 variables, fitted using GS + 9 software, was subjected to simple Kriging interpolation based on model parameters (Range, Nugget, Sill). Finally, the sequential Gaussian conditional simulation was completed using the “Gaussian Geostatistical Simulation” tool in ArcGIS 10.8. Through repeated experiments, the number of simulations was sequentially set to 10, 25, 50, 75, 100, and 125. After comparative analysis, it was found that the number of simulations required for the stabilization of the mean variance of pixel values for different variables varied, as detailed in Table 3. To match the area scale of ICESat-2 footprint points, the resolution of the raster data for each ICESat-2 variable simulation was set to 15.06 m. The variables that had undergone normalization and normal transformation were then subjected to denormalization and inverse transformation, resulting in the final true simulation results.

4.3. Comparison Analysis of Model Accuracy

Among them, the model built with XGBoost is relatively stable and has the highest accuracy. It is the optimal model for the inversion of forest stock volume in Jingdong Yi Autonomous County. The ‘accuracy’ mentioned below is a comprehensive reflection of the model’s predictive performance. It was evaluated by comparing the model’s prediction results with the actual sample data and was jointly assessed using R² and rRMSE. The fitting accuracy of the XGBoost model is R² = 0.89, rRMSE = 10.5912. Its key hyperparameter settings are as follows: learning rate = 0.1, num_leaves = 20, max_depth = 4, min_child_samples = 1, min_split_gain = 2. The fitting accuracy of the LightGBM model is R² = 0.84, rRMSE = 16.4846. Its key hyperparameter settings are as follows: learning rate = 0.1, num_leaves = 45, max_depth = 10, min_child_samples = 1, min_split_gain = 2. The fitting accuracy of the Random Forest model is R² = 0.81, rRMSE = 20.3166. Its key hyperparameter settings are as follows: n_estimators = 30, max_depth = 7, min_samples_split = 2, min_samples_leaf = 1. The LightGBM model is slightly inferior to the XGBoost model, and the Random Forest model performs the worst, with a significantly larger rRMSE. The data modeling of ICESat-2/ATLAS is shown in Figure 6.

4.4. Inversion Results of Forest Stock Volume in Jingdong Yi Autonomous County Using ICESat-2

Utilizing the XGBoost-derived forest stock volume predictive model, we conducted spatial inversion of woody biomass across the study region. The model yielded quantitative estimates with a mean stock volume of 141.00 m³/hm² (ranging from 30.41 to 338.22 m³/hm²). These inversion results enabled the generation of a high-resolution spatial distribution map depicting forest stock volume patterns throughout Jingdong Yi Autonomous County’s forested areas. The forest stock volume in the study area is relatively high, but the distribution of the stock volume is uneven, and the regional differences are large, and the high values of the stock volume in the study area are mostly distributed in the northwestern mountain range and the southeastern part of the study area. The spatial distribution of forest stock volume is shown in Figure 7, and from the local comparison of the inversion results in Figure 8, it can be seen that the inversion results of LightGBM and XGBoost, which are of higher accuracy, are more consistent, and the local comparative analysis shows that the inversion values of the two low-precision models are overestimated compared with those of the XGBoost model.

5. Discussion and Conclusions

5.1. Discussion

This paper focuses on the feasibility of ICESat-2/ATLAS data for forest stock volume inversion in mountain forests, adopts the traditional, relatively mature Random Forest model and the widely used and fast LightGBM model and XGBoost model for mountain forest stock volume modeling, and compares the modeling accuracy and inversion results of the three different models. The findings demonstrate that the proposed methodology successfully overcomes the challenges posed by the study area’s rugged topography and extreme elevation variations, achieving accurate forest stock volume estimation. Specifically, effective forest stock volume inversion can be carried out for the forested areas in the study area based on ICESat-2/ATLAS data, the forest stock volume inversion model is constructed by extracting multidimensional feature parameters of the data, the feasibility of single data inversion of stock volume is systematically evaluated, and the three machine learning regression methods used have high inversion accuracy The three machine learning regression methods used all have high inversion accuracy and strong nonlinear fitting ability; the R² of the optimal model XGBoost reaches 0.89, rRMSE = 10.5912, which indicates that the method has obvious applicability in estimating and inverting forest stock volume and confirms the practical value of single-data inversion.

However, this study has not yet systematically analyzed the differential effects of different terrain conditions and forest types on the forest stock volume inversion model. Meanwhile, the current inversion results still have an accuracy bias due to data time inconsistency and shadow interference of mountain images. Future research will focus on solving the following problems:

(1) Reliability and uncertainty analysis of the results: The average forest stock volume obtained from the inversion of the optimal model XGBoost is 141.00 m³/hm², the statistical average stock volume of the 212 corner gauge control sample plots of the 2016 National Forest Resources Planning and Design Survey used is 139.3 m³/hm², and the standard deviation (SD) of the sample plot statistics is 69.5 m³/hm², while the absolute value of the inversion and the sample plot statistics are the same. The absolute deviation of the inversion value from the statistical value of the sample site did not exceed the SD of the sample site data, and the coefficient of determination of the model R² reached 0.89, indicating that 89% of the spatial variability of the storage volume could be explained, and that the model precision was acceptable in the range of the natural variability of the sample site. The above quantitative indexes comprehensively proved that the complex mountain forest stock volume inversion model constructed in this study has high inversion accuracy and the results are credible. However, there are still errors: ① In terms of the overall storage volume obtained from the inversion, the results are overestimated to a certain extent, which is greatly affected by the complex terrain environment, such as the inclusion of bare soil and rocky plots in the forest area of the broken terrain, the increase in the error of predicting the canopy height due to the photon signal of the slope, and so on. ② Secondly, the forest inventory data employed in this study were obtained through field measurements conducted during the 2016 survey campaign across all sample plots, and the satellite-mounted lidar data were collected in 2019. Over a three-year study period, the natural growth of dominant tree species in the research area contributed to continuous increases in forest stock volume, which to some extent heightened inversion challenges and reduced model accuracy. ③ The small number of sample plots in the study area may lead to the inability to fully cover the environmental gradient in the study area, resulting in the difficulty of the model to learn the real ecological relationship, and the variance of parameter estimation under small samples increased, and the stability of the model was reduced.

(2) The influence of the selection of feature variables on the inversion results: This research implements a rigorous comparative framework to evaluate three ensemble learning algorithms—XGBoost, LightGBM, and Random Forest (RF)—assessing their relative performance through standardized validation protocols, and carries out modeling using their respective feature importance indexes to reveal the multidimensional expression of the feature–target relationship through the differences in the feature importance assessment of different algorithms. At the same time, before modeling, according to the existing literature, to screen the light spot parameters that may have a greater contribution to the forest stock volume for sequential Gaussian conditional simulation spatial interpolation, eliminating the parameters with lower spatial interpolation accuracy and retaining the variables that can truly reflect the geospatial autocorrelation can further improve the accuracy of the modeling.

(3) Effects of spatial interpolation on light spot parameters: Sequential Gaussian conditional simulation (SGCS), as a geostatistical method, shows unique advantages in the spatial inversion of forest stock volume, and at the same time, brings several issues that are worth exploring. In this study, we used the SGCS method to integrate satellite-borne LiDAR data with auxiliary variables for forest stock volume mapping. SGCS is suitable for simulating forest stock volume in mountainous areas with complex topography through spatial correlation modeling driven by the variational function. The spatial interpolation using the ordinary kriging method was attempted in the pre-experimental stage, but the interpolation effect was not satisfactory, so the spatial interpolation of the satellite-borne LiDAR spots in the complex mountainous environment was switched to the method of sequential Gaussian conditional simulation. This choice of spatial interpolation method provides a triple advantageous path of accuracy–efficiency–reliability for the spatial analysis of forest resources, and it can avoid or minimize the banding effect brought by satellite-borne LiDAR data and improve the spatial interpolation accuracy. Future research will adopt higher precision spatial interpolation methods to further achieve a high degree of matching of complex terrain to optimize its forest stock volume model.

(4) Impact of a single data source on the inversion results: This research focuses on the application of a single starborne LiDAR data source, in contrast to existing studies that use multi-source data synergy. However, multi-source fusion methods face inherent limitations such as optical data saturation and prediction error transfer while improving accuracy. In contrast, this study carries out the analysis based only on the 2019 ICESat-2/ATLAS on-board lidar photon data, avoiding the problem of error superposition caused by multi-source data fusion. Future studies will explore how to effectively control the errors that may arise from the introduction of optical data while maintaining the advantages of a single data source.

(5) The contribution of spaceborne lidar to reducing the workload of ground data collection is not yet clear: Since this study requires the use of angular control plot data as the true values, quantitative comparisons of different scale plots have not been conducted yet. Only a performance comparison among different machine learning models was carried out using the same number of plots (212 plots), and the fixed samples make it impossible to quantitatively assess the potential for sample reduction and to prove whether it is feasible to achieve the same performance with less data. Future research will explore how to establish a forest stock volume model with fewer plots to reduce the workload of ground surveys.

5.2. Conclusions

In this study, the forest stock volume estimation was performed through remote sensing inversion techniques in topographically complex mountainous regions, characterized by significant elevation variations and rugged terrain features, aiming at solving the problem of insufficient accuracy of stock volume inversion in a highly heterogeneous surface environment. Taking Jingdong Yi Autonomous County in Yunnan Province as the study area, which is characterized by a large elevation gradient and high terrain fragmentation, 13 parameters were extracted from 212 angularly controlled sample plots of ICESat-2 light patches in the forest range of the study area, and 10 parameters were selected for spatial interpolation by sequential Gaussian conditional simulation. A Random Forest model, LightGBM model, and XGBoost model were constructed for forest stock volume in the study area, and the XGBoost model constructed with the parameters extracted from ICESat-2/ATLAS data after photon point cloud denoising and photon point cloud classification algorithms had a higher accuracy of inversion for forest stock volume, with an R² = 0.89. We used it to invert the forest volume in the study area. The average forest stock volume was 141.00 m³/hm², the maximum forest stock volume was 338.22 m³/hm², and model results identified 30.41 m³/ha as the minimum stock volume threshold, accompanied by complete spatial distribution mapping of volume values throughout the forested landscape. This study demonstrates that lidar technology provides forest parameter estimates with accuracy comparable to ground surveys. Systematic validation revealed high consistency (R² = 0.89, rRMSE = 10.5912) between ICESat-2/ATLAS-derived forest stock volume and field measurements. The proposed methodology offers a practical solution for forest stock volume estimation in complex mountainous terrain, particularly in areas with steep topography and limited access. These findings confirm the reliability of spaceborne lidar for large-scale forest monitoring and support the development of GIS-based forest management systems. The combined advantages of operational efficiency and measurement accuracy suggest strong potential for forestry applications.